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written by
Gary Gladding
published by
the University of llinois Physics Education Research Group

This interactive homework problem shows a graph of velocity versus time for a moving object and the user is asked to find the final position. The problem is accompanied by a sequence of questions designed to encourage critical thinking and conceptual analysis. It is part of a larger collection of interactive problems developed by the Illinois Physics Education Research Group.

Standards (11)

AAAS Benchmark Alignments (2008 Version)

2. The Nature of Mathematics

2A. Patterns and Relationships

9-12: 2A/H1. Mathematics is the study of quantities and shapes, the patterns and relationships between quantities or shapes, and operations on either quantities or shapes. Some of these relationships involve natural phenomena, while others deal with abstractions not tied to the physical world.

2C. Mathematical Inquiry

9-12: 2C/H3. To be able to use and interpret mathematics well, it is necessary to be concerned with more than the mathematical validity of abstract operations and to take into account how well they correspond to the properties of the things represented.

4. The Physical Setting

4F. Motion

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9. The Mathematical World

9C. Shapes

9-12: 9C/H1. Distances and angles that are inconvenient to measure directly can be found from measurable distances and angles using scale drawings or formulas.

12. Habits of Mind

12B. Computation and Estimation

6-8: 12B/M3. Calculate the circumferences and areas of rectangles, triangles, and circles, and the volumes of rectangular solids.

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.1 Make sense of problems and persevere in solving them.

Geometry (K-8)

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

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